As shown in the following picture, an AttributedString is drawn on a JPanel (500X500).
The FontMetrics.getStringBounds() of that AttributedString gives a
FontMetrics fontMetrics = graphics.getFontMetrics() returns a FontMetrics object based on the single font currently set on the graphics object. You are not changing the font used by graphics explicitly so it uses the default font designated for JPanel by the current L&F.
FontMetrics methods related to bounds calculation accept a "simple" CharacterIterator (which does not provide font information) instead of AttributedCharacterIterator (which does). Hence fontMetrics.getStringBounds() simply calculates the text bounds based on the single font of the same size.
You need to use java.awt.font.TextLayout to determine the proper bounds when using AttributedCharacterIterator with different fonts and font sizes:
TextLayout textLayout = new TextLayout(
text.getIterator(),
g.getFontRenderContext()
);
Rectangle2D.Float textBounds = ( Rectangle2D.Float ) textLayout.getBounds();
g.drawString( text.getIterator(), 50, 50 );
// lets draw a bounding rect exactly around our text
// to be sure we calculated it properly
g.draw( new Rectangle2D.Float(
50 + textBounds.x, 50 + textBounds.y,
textBounds.width, textBounds.height
) );